# Triplet Sum to Zero

Given an array of unsorted numbers, find all unique triplets in it that add up to zero.

Example 1:

`Input: [-3, 0, 1, 2, -1, 1, -2]Output: [-3, 1, 2], [-2, 0, 2], [-2, 1, 1], [-1, 0, 1]Explanation: There are four unique triplets whose sum is equal to zero.`

Example 2:

`Input: [-5, 2, -1, -2, 3]Output: [[-5, 2, 3], [-2, -1, 3]]Explanation: There are two unique triplets whose sum is equal to zero.`

# Solution

We will sort the array and then iterate through it taking one number at a time. Let’s say during our iteration we are at number ‘X’, so we need to find ‘Y’ and ‘Z’ such that X + Y + Z =0. At this stage, our problem translates into finding a pair whose sum is equal to “−X” (as from the above equation Y+Z==−X).

Another note is that we need to find all the unique triplets. To handle this, we have to skip any duplicate number. Since we will be sorting the array, so all the duplicate numbers will be next to each other and are easier to skip.

`function search_triplets(arr) {   arr.sort((a, b) => a - b);   const triplets = [];   for (let i = 0; i < arr.length; i++) {     if (i > 0 && arr[i] === arr[i - 1]) { // skip same element to avoid duplicate triplets       continue;     }     search_pair(arr, -arr[i], i + 1, triplets);   }    return triplets; }   function search_pair(arr, target_sum, left, triplets) {   let right = arr.length - 1;   while (left < right) {     const current_sum = arr[left] + arr[right];     if (current_sum === target_sum) { // found the triplet       triplets.push([-target_sum, arr[left], arr[right]]);       left += 1;       right -= 1;       while (left < right && arr[left] === arr[left - 1]) {         left += 1; // skip same element to avoid duplicate triplets       }       while (left < right && arr[right] === arr[right + 1]) {         right -= 1; // skip same element to avoid duplicate triplets       }     } else if (target_sum > current_sum) {       left += 1; // we need a pair with a bigger sum     } else {       right -= 1; // we need a pair with a smaller sum     }   } }   console.log(search_triplets([-3, 0, 1, 2, -1, 1, -2])); console.log(search_triplets([-5, 2, -1, -2, 3]));Output[ [ -3, 1, 2 ], [ -2, 0, 2 ], [ -2, 1, 1 ], [ -1, 0, 1 ] ] [ [ -5, 2, 3 ], [ -2, -1, 3 ] ]`

# Time complexity

Sorting the array will take O(NlogN). The `searchPair()` function will take O(N). As we are calling `searchPair()` for every number in the input array, this means that overall `searchTriplets()` will take O(NlogN+N​^2​​), which is asymptotically equivalent to O(N^2).